By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp...By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.展开更多
The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.
In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. ...In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. A new duality form is introducedand the duality theorems are established.展开更多
In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtain...In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.展开更多
The sparse linear programming(SLP) is a linear programming problem equipped with a sparsity constraint, which is nonconvex, discontinuous and generally NP-hard due to the combinatorial property involved.In this paper,...The sparse linear programming(SLP) is a linear programming problem equipped with a sparsity constraint, which is nonconvex, discontinuous and generally NP-hard due to the combinatorial property involved.In this paper, by rewriting the sparsity constraint into a disjunctive form, we present an explicit formula of the Lagrangian dual problem for the SLP, in terms of an unconstrained piecewise-linear convex programming problem which admits a strong duality under bi-dual sparsity consistency. Furthermore, we show a saddle point theorem based on the strong duality and analyze two classes of stationary points for the saddle point problem. At last,we extend these results to SLP with the lower bound zero replaced by a certain negative constant.展开更多
In this paper, we consider the existence for periodic solutions of nonau- tonomons second-order differential systems with （q,p）-Laplacian by using the least action principle and the minimax methods.
基金This work was supported by the Foundation of First Period of Key Basic Research sponsored by the Department of Science and Technology of China(Grant No.2003CCA02400)National Natural Science Foundation of China(Grant No.10471029)by Natural Science Foundation of Guangdong Province(Grant No.04300034).
文摘By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.
文摘The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.
文摘In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. A new duality form is introducedand the duality theorems are established.
文摘In this paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fam Ky inequality is given. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.
基金supported by National Natural Science Foundation of China(Grant Nos.11431002,11771038 and 11728101)the State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University(Grant No.RCS2017ZJ001)China Scholarship Council(Grant No.201707090019)
文摘The sparse linear programming(SLP) is a linear programming problem equipped with a sparsity constraint, which is nonconvex, discontinuous and generally NP-hard due to the combinatorial property involved.In this paper, by rewriting the sparsity constraint into a disjunctive form, we present an explicit formula of the Lagrangian dual problem for the SLP, in terms of an unconstrained piecewise-linear convex programming problem which admits a strong duality under bi-dual sparsity consistency. Furthermore, we show a saddle point theorem based on the strong duality and analyze two classes of stationary points for the saddle point problem. At last,we extend these results to SLP with the lower bound zero replaced by a certain negative constant.
基金The NSF (10871059 and 10671028) of Chinathe Fundamental Research Founds (B09020181) for the Central Universities
文摘In this paper, we consider the existence for periodic solutions of nonau- tonomons second-order differential systems with （q,p）-Laplacian by using the least action principle and the minimax methods.
